Related papers: The Piranha algebraic manipulator
DSPSR is a high-performance, open-source, object-oriented, digital signal processing software library and application suite for use in radio pulsar astronomy. Written primarily in C++, the library implements an extensive range of modular…
Algencan is a well established safeguarded Augmented Lagrangian algorithm introduced in [R. Andreani, E. G. Birgin, J. M. Mart\'{\i}nez and M. L. Schuverdt, On Augmented Lagrangian methods with general lower-level constraints, SIAM Journal…
In this paper we provide a case study of the use of relatively sophisticated mathematics and algorithms to redefine and adapt a simple traditional game/puzzle to exploit the computational power of smart devices. The focus here is not so…
We develop an operator algebraic framework for generalized Cardano polynomials and show how their structure naturally leads to an operator formulation of Cardano method that is compatible with tools and concepts from quantum information…
Quaternion symmetry is ubiquitous in the physical sciences. As such, much work has been afforded over the years to the development of efficient schemes to exploit this symmetry using real and complex linear algebra. Recent years have also…
Quantum algorithms have begun to surpass classical ones in several computation fields, yet practical application remains challenging due to hardware and software limitations. Here, we introduce a quantum algorithm that quadratically…
This paper proposes a novel approach to solving nonlinear programming problems using a sharp augmented Lagrangian method with a smoothing technique. Traditional sharp augmented Lagrangian methods are known for their effectiveness but are…
This article deals with OLAP systems based on multidimensional model. The conceptual model we provide, represents data through a constellation (multi-facts) composed of several multi-hierarchy dimensions. In this model, data are displayed…
Fully automatic worst-case complexity analysis has a number of applications in computer-assisted program manipulation. A classical and powerful approach to complexity analysis consists in formally deriving, from the program syntax, a set of…
In this paper, we present a new hypercomplex number system, Trinition, that has an unusual structure of commutativity, noncommutativity, nonassociativity, and deformability.
In this paper, we will demonstrate how to use a nonlinear polyhedral constrained optimization solver called the Polyhedral Active Set Algorithm (PASA) for solving a general singular control problem. We present methods of discretizing a…
Probabilistic behavior is omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of various reasons, like uncertain environments, or fundamental properties of nature. In this paper, we…
A theorem of Christol states that a power series over a finite field is algebraic over the polynomial ring if and only if its coefficients can be generated by a finite automaton. Using Christol's result, we prove that the same assertion…
An 'arithmetic circuit' is a labeled, acyclic directed graph specifying a sequence of arithmetic and logical operations to be performed on sets of natural numbers. Arithmetic circuits can also be viewed as the elements of the smallest…
An algebraic characterization of the property of approximate controllability is given, for behaviours of spatially invariant dynamical systems, consisting of distributional solutions, that are periodic in the spatial variables, to a system…
A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has…
We establish new upper bounds for the numerical radius of bounded linear operators on a complex Hilbert space by introducing weighted geometric means of the modulus of an operator and its adjoint. This approach yields a family of…
We present Bill2d, a modern and efficient C++ package for classical simulations of two-dimensional Hamiltonian systems. Bill2d can be used for various billiard and diffusion problems with one or more charged particles with interactions,…
Given any square matrix or a bounded operator $A$ in a Hilbert space such that $p(A)$ is normal (or similar to normal), we construct a Banach algebra, depending on the polynomial $p$, for which a simple functional calculus holds. When the…
We introduce a general systematic procedure for solving any binary-input binary-output game using operator algebraic techniques on the representation theory for the underlying group, which we then illustrate on the prominent class of tilted…